Two-Loop Gluon-Condensate Contributions To Heavy-Quark Current Correlators: Exact Results And Approximations

Details Two-Loop Gluon-Condensate Contributions To Heavy-Quark Current Correlators: Exact Results And Approximations Two-Loop Gluon-Condensate Contributions To Heavy-Quark Current Correlators: Exact Results And Approximations

1994-03-11

arxiv.org/abs/hep-ph/9403274v1

Phys.Lett.B329:103-110,1994

Physics

High Energy Physics

High Energy Physics - Phenomenology

9 pages

Scientific paper

10.1016/0370-2693(94)90524-X

The coefficient functions of the gluon condensate $$, in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of $z=q^2/4m^2$. In the limiting cases $z\to0$, $z\to1$, and $z\to-\infty$, comparisons are made with previous partial results. Approximation methods, based on these limiting cases, are critically assessed, with a view to three-loop work. High accuracy is achieved using a few moments as input. A {\em single} moment, combined with only the {\em leading} threshold and asymptotic behaviours, gives the two-loop corrections to better than 1% in the next 10 moments. A two-loop fit to vector data yields $<\frac{\alpha_{\rm s}}{\pi}G^2>\approx0.021$ GeV$^4$.

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